Solve for $x$ and $y$ using elimination. ${-3x-2y = -17}$ ${5x+2y = 23}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $2x = 6$ $\dfrac{2x}{{2}} = \dfrac{6}{{2}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-3x-2y = -17}\thinspace$ to find $y$ ${-3}{(3)}{ - 2y = -17}$ $-9-2y = -17$ $-9{+9} - 2y = -17{+9}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {5x+2y = 23}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ + 2y = 23}$ ${y = 4}$